A Perturbation Calculation of the Elastic Scattering of Electrons By Hydrogen At

Cover A Perturbation Calculation of the Elastic Scattering of Electrons By Hydrogen At
A Perturbation Calculation of the Elastic Scattering of Electrons By Hydrogen At
Sidney Borowitz
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37) (7. 3B) (7. 39) N . - 8nk^n^(l - e) | a^(^^ N- Bnk^n^d - c) A(A-B) N, = I6n k^(ik^n^)(l - 6) A(A-B)^ Equation (7»37) in^ be integrated with respect to X most simply by noting 3 that the limit i is small compared to k and that A^ - q + X S q \ '\ k^- k^+ X^- 2iXk ^ - 2iXk no o o - UO - N = - 8iik^n^(l-e) [ -5- '^^^ |o q (-2ik X) (7. 1tC) ° 6n(ik^n^)(l-e) ^ Substituting the values of A and A-B into Eqs, (7. 38) and (7. 39), and noting that n^= l/ik, we finally obtain 6n(l- s) (7. I4I) N ^ (7.... 1:2) N3 = - I ^1%:^ z-? 1 :>\ M _ 16 n( l- e) (7. 1;3) \ •= - "5 5-- Insertion of these values into Eq. (7. 6) for the scattering amplitude yields (7. 10*) f' - 77 -^ (1-e) .
^ ' q k c Since .
1-e = T— cos © = cos © o q^ = 2k^ (1-cos e) = hk^ti, o o ' (7. 1:14) may be vn?itten as ^ 27k^ (1-cos ©) 271r (7. 1, c;) / . 8>^, i °o^Q » i^y^. I fhr^") The scattered amplitude f (cf. (2. 10)) has been worked out exactly by Corinaldesi and Trainor"^"^; their result is . La - Equation (7»i)6) differs considerably from our results} the energy variation is of order -» whereas our result gives — y • In addition, the angular variation o o for the asymmetric perturbation is opposite to that given by the symmetric per- turbation.


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